GRE Math : How to find out when an equation has no solution
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Example Questions
Example Question #52 : Algebra
Quantity A:
Quantity B:
The two quantities are the same.
Quantity A is greater.
Quantity B is greater.
The relationship cannot be determined.
Quantity A is greater.
To solve this problem, expand each function described by Quantities A and B:
Quantity A:
Quantity B:
Now note that Quantities A and B only differ in that Quantity A is greater by 
Since we are told that 
Example Question #11 : How To Find Out When An Equation Has No Solution
Quantity A:
Quantity B:
The two quantities are equal.
Quantity A is greater.
Quantity B is greater.
The relationship cannot be determined.
Quantity A is greater.
Rather than manually finding common denominators and adding the fractions together, realize that
Since
Quantity A must be greater, and this can be seen without actually calculating its value.
Example Question #12 : How To Find Out When An Equation Has No Solution
Approximately, what was the percent growth of Beetleton's GDP from 2009 to 2010?
Percent growth is given as:
For Beetleton, this can be expressed as (in terms of billions of US dollars):
Example Question #51 : Gre Quantitative Reasoning
The sum of two integers is 
Let us write down what we are told in mathematical terms, designating the smaller integer as 
The sum of the two integers is 
And the larger integer is 
Writing the first equation in terms of 
Which allows us to find 
Thus, the positive difference between the two is found as
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